Chapter 7.5, Problem 27E

To determine

To find the increase in percent of new amount by which it will return to its original amount.

Answer to Problem 27E

To return to the original amount, new amount has to increase by $300\%$ .

Explanation of Solution

Given information:

An original amount is decreased by $75\%$ .

Formula used:

New amount $=$ Original amount $-$ Amount of decrease.

  $\text{Percent of change, }p\%=\frac{\text{Amount of increase or decrease}}{\text{Original amount}}$ .

Calculation:

Lets consider that original number be $100$ than,

To find the new amount, first multiply the percent of change by the original amount to

find the amount of change. Then decrease the original amount by the amount of change.

New amount $=$ Original amount $-$ Amount of decrease

  $\begin{array}{l}=100-75\%\times 100\left[\text{Substitute}\right]\\ =100-0.75\times 100\left[\text{Write percent as a decimal}\right]\\ =25\left[\text{Evaluate}\text{.}\right]\end{array}$

The new amount after deduction of $75\%$ from the original amount is $25$ .

Amount of decrease $=$ Original amount $-$ New amount

  $\begin{array}{l}=100-25\left[\text{Substitute}\right]\\ =75\left[\text{Subtract}\right]\end{array}$

Now,

To return to the original amount we have to add the new amount with amount of decrease

  $25+75=100\left[\text{Add}\right]$

So consider the new amount as original amount and amount of decrease as amount of

increase in order to find the increase percent.

Therefore,

  $\begin{array}{l}\text{Percent of change, }p\%=\frac{\text{Amount of increase or decrease}}{\text{Original amount}}\\ p\%=\frac{75}{25}\left[\text{Substitute}\right]\\ p\%=\frac{3}{1}\left[\text{Divide}\right]\\ p\%=\text{300\% }\left[\text{Write fraction as a percent}\right]\end{array}$

Hence,

To return to the original amount, new amount has to increase by $300\%$ .